Leonhard Euler was Born in Basel on April 15, 1707. When he was one the family moved to Riehen, a town near Basel, where his father became a pastor. His father taught him elementary mathematics as a child. He entered the University of Basel at age 14. Euler's childhood home is shown in Figure 2a and the University of Basel is the building in the foreground of Figure 2b. His father's goal was for him to study theology and become a pastor. While at the university he met the famous mathematician Johann Bernoulli. In Euler's own words
… I soon found an opportunity to be introduced to a famous professor Johann Bernoulli. … True, he was very busy and so refused flatly to give me private lessons; but he gave me much more valuable advice to start reading more difficult mathematical books on my own and to study them as diligently as I could; if I came across some obstacle or difficulty, I was given permission to visit him freely every Sunday afternoon and he kindly explained to me everything I could not understand …
In 1723 (at age 16) Euler completed his Master's degree in philosophy. In his thesis he compared and contrasted the philosophical ideas of Descartes and Newton. He began the study of theology in the fall of 1723. However, he was still strongly attracted to mathematics. Johann Bernoulli finally convinced his father to allow him to change to mathematics. In spite of this change of vocation, his Christian faith remained strong throughout his life. He graduated in 1726. While in school he became close friends with the Bernoulli brothers Johann II, Daniel, and Nicolaus (sons of Johann). He was especially close to Daniel. In 1727 he won second place in the contest for the Grand Prize of the Paris Academy with an article on the best placement of masts on a ship. This was amazing since he, at this time, had never seen a ship. He would later win the Grand Prize twelve times.
The Bernoulli brothers, Daniel and Nicolaus, went to Russia and joined the Saint Petersburg Academy of Sciences in 1725, two years after it had been founded by Catherine I the wife of Peter the Great. Nicolaus Bernoulli could not handle the harsh Russian climate, and died prematurely in 1726. Euler was invited to Saint Petersburg in 1727. He was originally recruited for a position in the physiology division, but through the requests of Daniel Bernoulli and Jakob Hermann, Euler was appointed to the mathematical-physical division. The Saint Petersburg Academy of Sciences is shown in Figure 3.
The Saint Petersburg Academy of Sciences was established in order to bring Russia up to the same level in Science as other countries in Europe. Many talented scientists from other countries were imported to staff the Academy. They were given great freedom to pursue their research. Contrary to most of the foreign members of the Academy Euler quickly learned to read, write, and speak the Russian language. In 1732 the youngest Bernoulli brother, Johann II, came to Saint Petersburg and a year later he and Daniel decided to return to Switzerland. Daniel was offered a professorship in both Anatomy and Botany at the University of Basel. Their departure saddened Euler as they were his closest friends. Euler took over Daniel's chair in mathematics at the Saint Petersburg Academy. In December of 1733 Euler married a native Swiss of the same age, Catherine Gsell, the daughter of a painter from the St Petersburg Gymnasium. Euler and his family remained in Russia until 1741. While in Russia Euler solved the 91-year-old Basel problem in infinite series, namely, finding an exact sum of the infinite series $1 + 1/2^2 + 1/3^2 + 1/4^2 +\cdots$. In the process of solving this problem he developed what is now called the Euler-Maclaurin summation formula. This summation formula often improved the convergence rate of convergent infinite series and sometimes converted divergent series to convergent ones. He also made valuable contributions to number theory, the theory of partitions, mechanics, acoustics, and naval science. Toward the end of his stay in Russia, Euler lost the sight in one eye, possibly as the result of a fever.
Political unrest in Russia led to a tense working environment at the St. Petersburg Academy, prompting Euler to accept an invitation from Frederick the Great of Prussia to join his Royal Academy at Berlin in 1741. A drawing of the Academy is shown in Figure 4.
Frederick was enamored with everything French. In particular, he was drawn to the famous French philosopher Voltaire who made frequent visits to Frederick's court. Both Frederick and Voltaire ridiculed Euler's Christian faith. However, Euler was too famous as a mathematician for Frederick to replace him. Frederick asked Euler to tutor one of his nieces in the physical sciences and Euler agreed. This resulted in a series of over 200 letters that have been collected under the title Letters of Euler to a German Princess on Different Subjects in Natural Philosophy. These letters explained in laymen's language the basic concepts of physics as well as Euler's views on philosophy and theology. These letters were later published by the Saint Petersburg Academy in two large illustrated volumes. This work was tremendously popular with the general public and went through many editions. It was translated into French, English, German, Swedish, Italian, Danish, and Spanish. In the 25 years that Euler spent in Berlin he made important discoveries in the Calculus of Variations, established Euler's Identity for Complex Numbers, produced two treatises in analysis (Introduction to the Analysis of the Infinite in 1748 and Foundations of Differential Calculus, with Applications to Finite Analysis and Series in 1755), and explored key concepts in algebra such as solutions of polynomial equations and the Fundamental Theorem of Algebra.
In 1766 he accepted the invitation of Catherine the Great to return to the Saint Petersburg Academy. Shortly after returning, he lost sight in his remaining good eye following cataract surgery. He was virtually blind for the last seventeen years of his life. After losing the ability to see he commented
Now I will have less distraction.
In spite of his handicap, Euler's productivity never declined. He used his exceptional memory and the ability to perform calculations in his head to compose close to 400 additional manuscripts. He either wrote his results in large letters on a slate or dictated them to his sons or a secretary. In 1771 a fire destroyed Euler's home and he barely escaped with his life. Most of his manuscripts were rescued. In 1773 he lost his wife of 40 years. He married his wife's half-sister three years later. His two adult daughters died just prior to his own death. He died of a stroke on September 18, 1783 while engaged in his work. A picture of his tomb is shown in Figure 5. At his death the St. Petersburg Academy Journal had such a massive backlog of his work to publish that it took them another 48 years to complete.
During his second tour in St. Petersburg he produced influential works in integral calculus, algebra, dioptrics, navigation, and the theory of lunar motion.